A168200 a(n) = 3*n - a(n-1) + 1, with a(1)=4.

4, 3, 7, 6, 10, 9, 13, 12, 16, 15, 19, 18, 22, 21, 25, 24, 28, 27, 31, 30, 34, 33, 37, 36, 40, 39, 43, 42, 46, 45, 49, 48, 52, 51, 55, 54, 58, 57, 61, 60, 64, 63, 67, 66, 70, 69, 73, 72, 76, 75, 79, 78, 82, 81, 85, 84, 88, 87, 91, 90, 94, 93, 97, 96, 100, 99, 103, 102, 106, 105

Offset: 1

Author

Vincenzo Librandi, Nov 20 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1100
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Magma

[(6*n+5-5*(-1)^n)/4: n in [1..70]];

Mathematica

RecurrenceTable[{a[1]==4,a[n]==3n-a[n-1]+1},a,{n,70}] (* or *) LinearRecurrence[{1,1,-1},{4,3,7},80] (* Harvey P. Dale, Jul 31 2014 *)

PARI

a(n)=(6*n+5-5*(-1)^n)/4 \\ Charles R Greathouse IV, Jan 11 2012

Formula

a(n) = (6*n + 5 - 5*(-1)^n)/4. - Jon E. Schoenfield, Jun 24 2010

From Joerg Arndt, Apr 24 2011: (Start)

a(n) = +1*a(n-1) + 1*a(n-2) - 1*a(n-3).

G.f.: x*(4-x)/(1-x-x^2+x^3) = x*(4-x)/((1+x)*(1-x)^2). (End)

a(n) = floor(3*(n+1)/2)-(-1)^n. - Wesley Ivan Hurt, Sep 12 2017

Sum_{n>=1} (-1)^n/a(n) = 1 - Pi/(6*sqrt(3)) - log(3)/2. - Amiram Eldar, Feb 23 2023